Difficult Math Problem #85 - Probability - The Beat The GMAT Forum

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Difficult Math Problem #85 - Probability

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800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pm; Thanked: 11 times; Followed by:5 members

Difficult Math Problem #85 - Probability

by 800guy » Wed Jan 10, 2007 9:06 am

Brad flips a two-sided coin 8 times. What is the probability that he gets tails on at least 7 of the 8 flips?

A) 1/32

B) 1/16

C) 1/8

D) 7/8

E) none of the above

OA coming after a few people try to answer. Source: Difficult Math Problems doc on this forum

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Source: Beat The GMAT — Problem Solving | Wed Jan 10, 2007 9:06 am

Argen: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Jan 07, 2007 6:14 pm; Thanked: 1 times

by Argen » Wed Jan 10, 2007 10:49 am

Using the bernoulli distribution, lets add p(getting 7 tails) + p(getting 8 tails):

(8C7)*(0.5^7)*(0.5) + (8C8)*(0.5^8) = 8/(2^8) + 1/(2^8) = 9/256

It's also the same as the probability of getting at most 1 head. We calculate p(at most 1 head) = p(0 heads) + p(1 head):

(8C0)*(0.5^0)*(0.5^8) + (8C1)*(0.5^1)*(0.5^7) = 1/(2^8) + 8/(2^8) = 9/256

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800guy: Master | Next Rank: 500 Posts; Posts: 354; Joined: Tue Jun 27, 2006 9:20 pm; Thanked: 11 times; Followed by:5 members

OA

by 800guy » Fri Jan 12, 2007 12:31 am

OA

Number of ways 7 tails can turn up = 8C7
the probability of those is 1/2 each
Since the question asks for at least 7, we need to find the prob of all 8 tails - the number of ways is 8C8 = 1
Add the two probabilities
8C7*(1/2)^8 = 8/2^8 -- for getting 7
Prob of getting 8 tails = 1/2^8
Total prob = 8/2^8+1/2^8 = 9/2^8

Ans is E.

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ashish1354: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Jul 30, 2008 9:52 am; Thanked: 4 times

can we solve the problem without combinatorics ?

by ashish1354 » Sun Sep 21, 2008 12:17 am

i think i am being asked for probability of 7 tails & probability of getting 8 tails in 8 throws
total possible outcomes=2(possible outcomes on any throw)*8(total throws)
=16

probability that he gets tails on at least 7 of the 8 flips=7/16*8/16=7/32
but this is wrong answer. can someone suggest how to calculate the right answer without combinatorics or suggest how to use Bernoulli distribution (i do not understand whether it is used to combine probabilities or it is used after we calculate total possible and favorable events)

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stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Sun Sep 21, 2008 12:29 pm

Ashish, others,

Answer without formulas:

Totals 8 flips: possible arrangements = 2^8

we need 7 tails and 8 tails
in 8 ways we can have 7 tails [as 1 h can be at 8 places]
and
in 1 way we can have 8 tails

so favorable outcomes = 8+1 = 9
Total outcomes = 2^8 = 256

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